An (A, B)-cyclic submodule M is generated by the states of one single traje
ctory of a linear control system whose parameters come from a commutative r
ing. M is "finite", when it is generated by the states of a "deadbeat-contr
ol" process. Motivations and basic properties of such modules are given and
among several further results it is shown that the family of finite (A, B)
-cyclic submodules is an invariant which (e.g., over polynomials) can be de
termined by an appropriate Grobner basis computation. (C) 1999 Elsevier Sci
ence Inc, All rights reserved.